Approximate controllability of semilinear deterministic and stochastic evolution equations in abstract spaces. (English) Zbl 1084.93006

Mahmudov, Nazim I.

SIAM J. Control Optimization 42, No. 5, 1604-1622 (2003).

In the paper semilinear, infinite-dimensional, continuous-time control systems are considered. Fundamental definitions concerning approximate and stochastic controllability in infinite-dimensional control systems are recalled and discussed. Using methods and theorems taken directly from functional analysis, sufficient conditions for approximate controllability are formulated and proved. These conditions require verification of approximate controllability of associated linear control system. Moreover, two illustrative examples are also included. Similar problems have been considered in [J. Klamka, Control Cybern. 29, No. 1, 153–165 (2000; Zbl 1011.93001)].

Reviewer: Jerzy Klamka (Gliwice)

MSC:

93B05	Controllability
93C25	Control/observation systems in abstract spaces
93C10	Nonlinear systems in control theory

Keywords:

controllability; nonlinear control systems; infinite-dimensional systems; stochastic evolution equations; continuous-time systems; fixed-point theorems; nonlinear semigroup theory; symmetric operators; Schauder fixed point theorem; contraction mapping principle; semilinear evolution equations

Citations:

Zbl 1011.93001